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Concept explainers
The fraction of the Sun’s mass that will be converted into helium over the next 5 billion years, if it is assumed that the current rate of the hydrogen fusion remains constant. Also, discuss its effect on the overall chemical composition of the Sun.
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Answer to Problem 10Q
Solution:
Explanation of Solution
Given data:
The current rate of the hydrogen fusion in the Sun remains constant.
The time is 5 billion year.
Formula used:
The expression for the mass-energy equation is written as:
Here, E is the total energy
Explanation:
The Sun’s luminosity is
The total energy radiated by the Sun in 5 billion year is calculated as,
Recall the expression of the mass-energy equation.
Rearrange the above expression for
Substitute
Only .7% of the mass is transformed into energy at the time of conversion of the hydrogen into helium. So, the amount of hydrogen used in Sun’s energy production over the next 5 billion year is,
The mass of the Sun is
The present composition of the Sun is 74% hydrogen, 25% helium, and 1% heavy elements.
Thus, the mass of each component in Sun is,
The mass of hydrogen is,
The mass of helium is,
The mass of heavy elements is,
Over 5 billion year the composition of the Sun is as:
The composition of hydrogen is,
The fraction of the sun’s mass that will be hydrogen in 5 billion year is,
It is 69% of the Sun’s mass.
Now, the composition of helium is,
The fraction of the sun’s mass that will be helium in 5 billion year is,
It is 30% of the Sun’s mass.
Conclusion:
Therefore, the mass converted into energy in 5 billion year is
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Chapter 16 Solutions
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